Chapter - 3 Characteristics of sea and swell
Chapter 3:
Characteristics of sea and swell – Influence of
southern Ocean winds
3.1 Introduction
This chapter presents, characteristics of sea and swell waves in relation to the
influence of southern swell off East Coast of India. The tides in this region are
semi-diurnal, mean spring tidal range is around 1.43 m and neap tidal range is
0.54 m. The location of the wave spectrum measurement site is shown in figure
3.1.
The waves were measured using Directional Wave Rider Buoy (Datawell) from
1st June 2009 to 31st May 2010 with an interval of 30 min. The time reference in
this chapter is in Coordinated Universal Time (UTC). The buoy was anchored at
20 meters depth off Gangavaram coast (17° 38.011′ N, 83° 15.946′ E), south of
Visakhapatnam harbor. The coastline aligned in WSW direction with almost
parallel offshore bathymetry contours. The shoreline was characterized by
different types of sediment characteristics like sand with different grain size,
scattered rocky out crops, rocky protrusions and sand dunes. The wave spectrum
was obtained through Fast Fourier transform (FFT). Heave was measured in the
range of -20 to 20 m with a resolution of 1 cm and an accuracy of 3%.
42
Chapter - 3 Characteristics of sea and swell
Figure 3.1: Location of the Directional Wave Rider Buoy
3.2 Separation of sea and swell using Steepness method
The raw data was processed to compute SWH and Zero upcross wave period
(Tz) following the method of Tucker (1963). SWH and Tz are defined as
SWH  4 m0
(3.1)
m0
m2
Tz 
(3.2)
Where m0 and m2 are the spectral moments and are computed from
mn 
fu
f
n
S ( f )df
n = 0, 2
(3.3)
fl
43
Chapter - 3 Characteristics of sea and swell
Where mn is the n-th order spectral moment, S(f) is the spectral energy density
at frequency f, fι is the lower frequency limit and fu is the upper frequency
limit. The high frequency cut off was set at 0.58 Hz and low frequency cut off
was set at 0.03 Hz with 0.005 resolution. Other parameters obtained from
spectral analysis were spectral width parameter (ε) (Cartwright and LonguetHiggins, 1956), spectral narrowness parameter (ν) and spectral peakedness
parameter (Qp) (Goda, 1970) are defined below.
  1
m22
m0 m4

m0 m2
1
m12
Qp 
2
m02
(3.4)
(3.5)
fu
 fS
2
( f )df
(3.6)
fl
Where m1 and m4 are calculated from equation (3.3) with n = 1 and 4
respectively. The wave steepness method adopted by National Data Buoy
Center (NDBC) was used to separate the sea and swell components from the
wave spectra (Gilhousen and Hervey, 2001). Estimation of sea and swell were
made by calculating the separation frequency (fs) using steepness method that
partitions the wave spectrum into its sea and swell parts. The respective parts
of the spectrum were then used to compute significant wave height (Hss and
Hsw), zero crossing period (Tss and Tsw) and mean direction (θss and θsw) of sea
and swell portions respectively. The steepness function ξ(f) and separation
frequency (fs) is given by
( f ) 
8m2 ( f )
g m0 ( f )
(3.7)
44
Chapter - 3 Characteristics of sea and swell
Figure 3.2: Typical plot of steepness function versus frequency.
f s  Cf m
(3.8)
Where fm is the frequency of maximum of ξ(f), and C=0.75 is an empirically
determined constant. Figure 3.2 shows the typical plot of steepness function. The
frequency corresponding to the maximum spectral energy density is referred as
spectral peak frequency (fp) and was estimated from the wave spectrum. Height of
the highest wave (Hmax) was estimated from zero-crossing analysis. The spectral
width (ε) and narrowness parameter (ν) varied from 0 to 1, and had smaller values
for narrower spectra.
From the measured wave spectrum data the separation frequencies (fs) were
calculated using steepness method (equation 3.8). Wave parameters were derived
from the each part separately i.e., swell parameters from lower frequency part and
sea parameters from higher frequency part (Figure 3.3).
45
Chapter - 3 Characteristics of sea and swell
Figure 3.3: Typical graph of wave spectrum and separation of sea and swell parts.
Spectral moments for swell
(3.9)
Spectral moments for sea
(3.10)
Where fl is lower frequency limit, fs is separation frequency and fu is upper
frequency limit. The integral parameters such as significant height of sea (Hss),
zero up cross period of sea (Tzs), significant height of swell (Hsw) and zero up
cross period of swell (Tzw) were calculated using Tucker (1963) method and
presented for each season in this section.
3.3 Characteristics of sea and swell
The wave data was examined for quality control prior to analysis. Initially the
abnormal data points were removed by observing graphically. Subsequently the
data was picked up with three hour time interval of standard synoptic hours (0, 3,
6, 9, 12, 15, 18 and 21hrs). The well sorted wave spectrum data was used to
derive the wave parameters using the methodology discussed as above. The
characteristics of sea and swell at measuring site and influence of swell from
south are discussed in detail during different seasons in the following sections.
46
Chapter - 3 Characteristics of sea and swell
3.3.1 Wave groups during summer monsoon (Jun to Aug)
The wave groups were presented as scatter plots during summer monsoon period
(Figure 3.4) of SWH vs Tz before and after separation of wave spectrum. It can be
clearly observed that prior to separation all data forms a close group with no
significant trend. After applying Steepness method, the sea and swell wave could
be clearly separated. Further, after separation it was seen that sea waves follows a
linear trend whereas no significant trend was observed in swell.
The summarized statistics of all the derived wave parameters for summer
monsoon are given in Table 3.1. The observed ranges for SWH were from 0.9 to
2.6 m and for Tz from 4.4 to 9.5 seconds. These observations were closely in
agreement with past studies which were reported the range of SWH was from 1 to
3 m (Chandramohan, Sanil Kumar and Nayak, 1991; Nayak, Chandramohan and
Sakhardande, 1992). After applying the steepness method on total wave spectrum
the wave groups were well separated as sea (high frequency waves) and swell
(low frequency waves) (Figure 3.4(b)). The distribution of sea waves was nearly
linear indicating higher corresponding to waves of longer time period and vice
versa.
In general the summer monsoon was characterized by strong winds resulting in
short wave with minimum amplitude of 0.2 m. However the swells generated by
distant storms have amplitudes from 0.5 to 2.3 m with a maximum time period of
14 sec. From figure 3.4(b) the swell waves are scatterly distributed and mean
period is about 9.5 sec. The deviation from mean value (standard deviation) of
Hss and Hsw is almost same, but standard deviation of Tzs is half of standard
deviation of Tzw.
This represents a wide spectrum of swell reaching from
different storms to the observation site.
47
Chapter - 3 Characteristics of sea and swell
Table 3.1: Summarized wave parameters during summer monsoon period (JJA).
Parameter
Significant wave height
Zero upcross period
Peak direction
Height of highest wave
Period of highest wave
Average height of 10%
highest waves
Average period of 10%
highest waves
Average height of 33%
highest waves
Average period of 33%
highest waves
Average height of all
waves
Average period of all
waves
Significant wave height
of sea
Zero upcross period of
sea
Significant wave height
of swell
Zero upcross period of
swell
Mean direction of sea
Mean direction of swell
Peak period
Peak directional spread
Spectral narrowness
Spectral width
Spectral peakedness
Significant steepness
Integral period
Mean period
Crest period
Calculated peak period
JJA
SWH
Tz
Dirp
Hmax
T(Hmax)
Minimum Maximum Average Stdev Anomaly
0.91
2.59
1.66
0.28
0.60
4.35
9.52
6.21
0.75
0.49
120.90
192.70
161.19 12.48
5.56
1.26
4.51
2.52
0.49
0.92
4.96
67.84
10.43
5.33
-0.77
H[1/10]
1.02
2.94
1.89
0.33
0.70
T(H[1/10])
6.90
37.10
10.10
3.24
-0.23
H[1/3]
0.80
2.40
1.51
0.27
0.57
T(H[1/3])
6.89
29.71
9.43
2.63
0.19
Hav
0.48
1.51
0.96
0.17
0.36
T(Hav)
4.89
20.88
7.01
1.58
0.47
Hss
0.19
1.79
0.85
0.26
0.31
Tzs
2.21
6.89
4.00
0.76
0.58
Hsw
0.53
2.28
1.35
0.28
0.48
Tzw
dms
dmw
Tp
Sprp
nu
eps
QP
Ss
TI
T1
Tc
Tpc
7.16
68.70
115.50
6.25
8.50
0.40
0.72
1.08
0.01
7.32
4.97
2.53
8.98
14.40
265.50
180.10
20.00
39.80
0.82
0.92
2.91
0.05
13.16
10.50
4.88
19.13
9.51
186.45
152.20
11.35
19.14
0.53
0.80
1.67
0.03
9.39
7.02
3.67
12.63
1.44
18.66
9.42
3.33
4.93
0.07
0.04
0.29
0.01
1.27
0.91
0.39
2.16
-0.22
28.81
3.03
-0.48
-2.91
-0.07
0.00
-0.05
0.01
-0.20
0.36
0.42
-1.46
48
Chapter - 3 Characteristics of sea and swell
Figure 3.4: Wave groups obtained from (a) total wave spectrum and (b) separated
spectrum of sea and swell during summer monsoon period.
The maximum value of the instantaneous heave (i.e., height of the highest wave
Hmax ) from all the recorded spectrum during this season is 4.5 m. Whereas the
maximum SWH recorded for this season was 2.6 m. Sathe et al. (1979) reported
that maximum SWH of about 2.3 m over western Bay of Bengal during summer
monsoon 1978. The waves predominantly approach the coast from the SE during
this period. The typical pattern of summer monsoon wave spectrum on 15th July
2009 was given in Figure 3.5. The highest peak of spectral density lies within the
frequency range of 0.05 to 0.15 Hz. This shows the dominance of swell
approaching from SSE direction. The shifting of high spectral density towards SW
direction shows the contribution of sea’s from SSW direction.
49
Chapter - 3 Characteristics of sea and swell
Figure 3.5: Typical wave spectrum on 15th July 2009.
3.3.2 Wave groups during post monsoon (Sep to Nov)
Figure 3.6(a) show the wave groups before separation in the post monsoon season
and are well distributed compared to summer. The large standard deviation of
SWH (0.45 m) and Tz and (1.66 sec) among all seasons show the occurrence of
waves with wide spectrum of frequencies (3.5 to 11 sec) and large range of wave
heights (0.5 to 2.6 m) during this season (Table 3.2). This is because of the
withdrawal of monsoon, the wind forcing drastically reduces from September to
November, which causes the generation waves with wide range of groups in this
season. The summarized wave parameters for post monsoon were given in
Table 3.2.
50
Chapter - 3 Characteristics of sea and swell
Table 3.2: Summarized wave parameters during post monsoon (SON).
Parameter
Significant wave
height
Zero upcross period
Peak direction
Height of highest
wave
Period of highest
wave
Average height of
10% highest waves
Average period of
10% highest waves
Average height of
33% highest waves
Average period of
33% highest waves
Average height of
all waves
Average period of
all waves
Significant wave
height of sea
Zero upcross period
of sea
Significant wave
height of swell
Zero upcross period
of swell
Mean direction of
sea
Mean direction of
swell
Peak period
Peak directional
spread
Spectral narrowness
Spectral width
Spectral peakedness
Significant
steepness
Integral period
Mean period
Crest period
Calculated peak
period
SON
Minimum Maximum Average Stdev
Anomaly
SWH
Tz
Dirp
0.46
3.54
78.80
2.62
11.11
185.60
1.12
6.44
155.47
0.45
1.66
13.96
0.06
0.72
-0.16
Hmax
0.62
3.83
1.68
0.68
0.08
T(Hmax)
4.20
70.70
11.93
6.79
0.73
H[1/10]
0.49
2.85
1.26
0.51
0.07
T(H[1/10])
4.96
43.37
11.15
4.10
0.82
H[1/3]
0.40
2.32
1.00
0.42
0.06
T(H[1/3])
4.73
34.63
10.16
3.65
0.92
Hav
0.24
1.51
0.63
0.26
0.03
T(Hav)
3.72
21.17
7.24
2.28
0.70
Hss
0.08
2.01
0.50
0.31
-0.05
Tzs
2.16
8.16
3.39
0.93
-0.03
Hsw
0.27
2.22
0.94
0.39
0.07
Tzw
6.00
17.17
9.99
1.78
0.26
Dms
46.90
327.00
151.20
60.88
-6.45
Dmw
Tp
110.10
3.33
190.10
20.00
148.56
12.32
12.57
2.96
-0.61
0.49
Sprp
Nu
Eps
QP
7.30
0.34
0.64
0.98
48.30
0.97
0.94
4.74
20.91
0.60
0.83
1.83
6.24
0.11
0.06
0.55
-1.14
0.00
0.02
0.11
Ss
TI
T1
Tc
0.00
6.17
3.92
2.29
0.05
14.83
12.25
5.73
0.02
10.24
7.49
3.43
0.01
1.94
1.91
0.64
0.00
0.65
0.83
0.19
Tpc
8.52
21.49
14.22
2.68
0.13
51
Chapter - 3 Characteristics of sea and swell
Figure 3.6: Wave groups obtained from (a) total wave spectrum and (b) separated
spectrum of sea and swell during post monsoon.
After the separation of the wave spectrum data into sea and swell components, the
distribution of wave groups were presented in figure 3.6(b). The distribution of
sea waves was in cone shape. It represents that as the Tz increases the range of
Hss increases. For instance, from figure 3.6(b) nearly at 5 sec period the range of
wave heights distributed from 0.5 m to 1.7 m, whereas at 2 sec the range is very
small. Swell waves were well scattered in this season. The distant wind forcing
like TSIO, ETSIO and due to reduced cross equatorial winds, different wave
groups with different frequencies and heights occurs. This is in agreement with
the previous studies (Young, 1994; Rajkumar et al., 2009; Sabique et al., 2012).
The height of the highest wave for this entire season was 3.8 m occurred in 8th
September, 2009. The average spectral bandwidth of 0.83 which is slight more
than that of summer represents the presence of waves with comparatively wide
range of frequencies. The typical pattern of post monsoon wave spectrum on 14th
October 2009 was given in Figure 3.7. This spectrum shows a clear indication of
52
Chapter - 3 Characteristics of sea and swell
swell wave dominance approaching from SSE direction with narrow band of
frequency (~ 0.05 to 0.1 Hz). Whereas sea’s were observed as less significant. A
large difference between Hss (0.5 m) and Hsw (0.94 m) also supports the well
identified dominance of swell during this season (Table 3.2).
Figure 3.7: Typical wave spectrum on 14th October 2009.
3.3.3 Wave groups during winter monsoon (Dec to Feb)
The wave groups in winter were closely packed as in summer. However, on the
lower side of the axes the close clustering of wave groups indicates that the sea
state is more or less same throughout the season (Figure 3.8(a)). Since the winter
monsoon was characterized by comparatively moderate winds over BoB with
limited fetch, that results in limited growth of waves. This causes the occurrence
of waves with low magnitudes of 0.6 m mean SWH and with very low standard
deviation of 0.2 m (Table 3.3). The separated sea and swell groups (Figure 3.8(b))
reveals very important information that the limited fetch causes the generation of
nearly same group of sea waves. This can be clearly understood by comparing the
sea wave groups of summer and winter season. The summarized wave parameters
for winter monsoon season were given in Table 3.3.
53
Chapter - 3 Characteristics of sea and swell
Table 3.3: Summarized wave parameters during winter monsoon (DJF).
Parameter
Significant wave
height
Zero upcross period
Peak direction
Height of highest
wave
Period of highest
wave
Average height of
10% highest waves
Average period of
10% highest waves
Average height of
33% highest waves
Average period of
33% highest waves
Average height of all
waves
Average period of
all waves
Significant wave
height of sea
Zero upcross period
of sea
Significant wave
height of swell
Zero upcross period
of swell
Mean direction of
sea
Mean direction of
swell
Peak period
Peak directional
spread
Spectral narrowness
Spectral width
Spectral peakedness
Significant steepness
Integral period
Mean period
Crest period
Calculated peak
period
DJF
Minimum Maximum Average Stdev
Anomaly
SWH
Tz
Dirp
0.20
2.50
78.80
1.32
8.00
210.90
0.60
4.92
150.48
0.20
1.02
19.63
-0.45
-0.80
-5.15
Hmax
0.31
2.24
0.90
0.31
-0.70
T(Hmax)
1.95
142.48
10.22
6.89
-0.98
H[1/10]
0.22
1.44
0.66
0.22
-0.53
T(H[1/10])
2.98
22.35
9.14
2.73
-1.19
H[1/3]
0.17
1.16
0.52
0.17
-0.43
T(H[1/3])
2.91
17.12
7.87
2.09
-1.37
Hav
0.11
0.72
0.33
0.11
-0.27
T(Hav)
2.64
10.64
5.44
1.15
-1.11
Hss
0.10
0.90
0.33
0.14
-0.21
Tzs
1.97
5.00
3.04
0.57
-0.39
Hsw
0.15
1.15
0.48
0.17
-0.39
Tzw
5.56
14.30
9.19
1.82
-0.54
dms
75.50
235.30
119.06
33.16
-38.58
dmw
Tp
114.70
2.56
188.50
20.00
146.60
11.79
12.21
3.17
-2.57
-0.04
Sprp
Nu
Eps
QP
Ss
TI
T1
Tc
11.80
0.33
0.47
0.91
0.01
4.74
2.69
1.99
65.70
1.03
0.93
4.50
0.05
13.56
9.90
4.09
26.04
0.64
0.79
1.64
0.02
9.17
5.85
2.87
7.93
0.12
0.07
0.45
0.01
1.84
1.33
0.38
3.99
0.04
-0.01
-0.09
0.00
-0.42
-0.81
-0.37
Tpc
7.18
26.04
14.66
3.78
0.58
54
Chapter - 3 Characteristics of sea and swell
Figure 3.8: Wave groups obtained from (a) total wave spectrum and (b) separated
spectrum of sea and swell during winter monsoon.
The linear spread of sea wave groups in summer indicates the presence of
comparatively wide range of waves, whereas in winter the sea wave groups exist
with small range. However, the occurrence of swell waves were in wide range of
time periods (5.6 to 14.3 sec) almost similar to summer, but the magnitude of the
waves was very low (0.15 to 1.15 m). The average spectral bandwidth parameter
of 0.79 was slightly low among all seasons, indicates that the waves with very
narrow band of frequencies exist in this season.
The typical pattern of winter
monsoon wave spectrum during 17th January 2010 was given in Figure 3.9. This
spectrum shows a well identified sea and swell parts from different directions.
Swell from SSE direction were more dominant with narrow band of frequency
(~ 0.05 to 0.1 Hz). Whereas sea’s from East were observed with a wide range.
55
Chapter - 3 Characteristics of sea and swell
Figure 3.9: Typical wave spectrum on 17th January 2010.
3.3.4 Wave groups during pre monsoon (Mar to May)
The number of data samples for this season were comparatively low, because of
buoy technical problems and the occurrence of AILA cyclone over BoB from 21 st
May to 26th May 2010. While doing quality checks, the data from 18th May 2010
to 31st May 2010 was eliminated to study the seasonal characteristics. The data
from March 2010 to 17th May 2010 with some gaps in the month of April 2010
was considered to explain the characteristics of sea and swell in this season. The
summarized wave parameters during this season were given in Table 3.4.
The wave groups during pre monsoon were closely packed with average SWH of
0.83 m and Tz of 5.15 sec (Figure 3.10(a)). The sea waves were distributed in
linear manner such that the standard deviation of Hss was 0.19 m, which is
slightly higher than that of winter, but lower than the summer and post monsoon
seasons.
However, the swell waves showed scattered distributtion with Tzw
ranged from 6.6 – 13.8 sec and Hsw from 0.3 – 1.31 m (Figure 3.10(b)) (Table
56
Chapter - 3 Characteristics of sea and swell
3.4). Hence the sea state was calm compared to summer and winter monsoons
while, slightly high compared to post monsoon.
Table 3.4: Summarized wave parameters during pre monsoon (MAM).
Parameter
Significant wave
height
Zero upcross period
Peak direction
Height of highest
wave
Period of highest wave
Average height of
10% highest waves
Average period of
10% highest waves
Average height of
33% highest waves
Average period of
33% highest waves
Average height of all
waves
Average period of all
waves
Significant wave
height of sea
Zero upcross period of
sea
Significant wave
height of swell
Zero upcross period of
swell
Mean direction of sea
Mean direction of
swell
Peak period
Peak directional
spread
Spectral narrowness
Spectral width
Spectral peakedness
Significant steepness
Integral period
Mean period
Crest period
Calculated peak period
(MAM)
SWH
Tz
Dirp
Minimum
Maximum Average
Stdev
Anomaly
0.37
2.96
132.20
1.45
9.52
355.80
0.83
5.15
156.01
0.22
1.04
14.79
-0.23
-0.57
0.38
Hmax
T(Hmax)
0.50
2.94
3.03
168.97
1.27
12.50
0.36
10.67
-0.33
1.29
H[1/10]
0.42
1.93
0.93
0.25
-0.26
T(H[1/10])
4.09
44.89
11.10
5.20
0.77
H[1/3]
0.34
1.34
0.73
0.20
-0.22
T(H[1/3])
3.86
36.97
9.58
4.37
0.34
Hav
0.20
0.87
0.46
0.13
-0.14
T(Hav)
3.29
25.64
6.48
2.64
-0.07
Hss
0.09
1.09
0.49
0.19
-0.06
Tzs
2.10
4.89
3.20
0.43
-0.23
Hsw
0.30
1.31
0.63
0.18
-0.24
Tzw
Dms
6.59
107.60
13.76
247.10
10.47
182.81
1.29
14.41
0.74
25.17
Dmw
Tp
120.70
3.85
205.70
25.00
149.47
11.81
10.59
2.69
0.29
-0.02
8.70
0.39
0.61
1.03
0.00
6.13
3.33
2.24
8.98
63.10
0.95
0.94
6.48
0.05
14.36
11.44
4.70
29.13
21.76
0.65
0.80
1.77
0.02
9.54
6.13
2.94
15.02
6.50
0.10
0.07
0.61
0.01
1.48
1.39
0.29
2.42
-0.29
0.05
-0.01
0.04
0.00
-0.06
-0.53
-0.31
0.94
Sprp
Nu
Eps
QP
Ss
TI
T1
Tc
Tpc
57
Chapter - 3 Characteristics of sea and swell
Figure 3.10: Wave groups obtained from (a) total wave spectrum and (b) separated
spectrum of sea and swell during pre monsoon.
The typical pattern of pre monsoon wave spectrum on 14th April 2010 was given
in Figure 3.11. The spectrum shows a mixed sea state condition with significant
contributions from sea as well as swell, approaching from South to SSE direction.
Figure 3.11: Typical wave spectrum on 14th April 2010.
The analysis of wave parameters during different seasons indicated that summer
monsoon was characterized by high waves with average SWH of 1.66 m which
was due to comparatively high winds. Winter monsoon was characterized with
58
Chapter - 3 Characteristics of sea and swell
low SWH of 0.6 m. This was well understood by several studies on wave
characteristics
over
TNIO
(Kesavadas,
Varkey
and
Ramaraju,
1979;
Chandramohan, Sanil Kumar and Nayak, 1991; Vethamony et al., 2000).
Kesavadas et al. (1979) reported that the predominant wave height off west coast
of India during fair weather season was 1 m, whereas during rough weather it was
2 m. A study based on ship reported wave data around the Indian coast showed the
dominance of 1to 3 m waves in summer monsoon and around 1 m in winter
monsoon (Chandramohan, Sanil Kumar and Nayak, 1991). Similar study using
altimeter data also revealed the occurrence of higher waves (> 5 m) during
summer monsoon and low waves ( < 3 m) during winter monsoon (Vethamony et
al., 2000). In the present study the standard deviation of SWH was maximum
(0.45 m) during post monsoon and minimum (0.2 m) during winter monsoon. This
minimum standard deviation and minimum Spectral width parameter (0.79)
showed that the sea state condition was calm throughout winter season. Swells
were dominating most of the period with comparatively high magnitudes.
From the discussion in above sections, it was clear that the contribution of swell to
the local ocean state was of very high significance. As the present measurement
site is situated off east coast of India, most of the distant swell waves approach
from south due to land boundaries on other three sides. Apart from monsoon
circulation, the well identified trade winds over south of the equator and extra
tropical southern ocean storm winds were the major sources for the occurrence of
long swell. Further the previous studies carried out by Rajkumar et al. (2009) and
Sabique et al. (2012) have also reported the probable propagation of these swells
from Extra Tropical South Indian Ocean (ETSIO). Therefore it is also essential to
59
Chapter - 3 Characteristics of sea and swell
estimate the time taken by these swells to reach the measurement site from
ETSIO. This can be achieved through lag correlation analysis.
3.4 Lag correlation analysis – significance of swells from ETSIO
In this section an attempt has made to calculate the time lag between ETSIO wind
variability and measured swell variability. As the wave celerity ( C ) in terms of
time period (T) was computed from Eqn. 3.11.
C = gT/2π
(3.11)
The analysis of Tz data showed an annual range from 5.6 to 17.2 sec. For the
annual range of Tz, the celerity of observed swell waves varied from 31.5 to 96.6
kmph respectively. Hence the minimum time taken by these swell to travel from
southern most end of 60˚ S to the buoy location (17˚ N) was estimated as 3.7 days
whereas it was observed that swell of maximum Tz takes 11.3 days. Based on this
theoretical approximation, lag correlation analysis was done between the
measured swell (Hsw) and spatially averaged ETSIO wind speed from a time lag
of 0 to 13 days.
The plot of correlation coefficient, r (solid blue line) and probability of r to
become zero, P (dashed green line) for first 13 days is given as Figure 3.12. The
x-axis indicates the time lag in days. The value of r varies between -1 and +1. The
values above 0.5 (+ve or -ve) were considered as reasonable correlation. The
value of P varies from 0 to 1. The P value close to zero indicates that the r is
statistically significant.
The time lag at which the maximum significant
correlation (rmax) occurs was identified as the time lag between Hsw and ETSIO
wind variability.
60
Chapter - 3 Characteristics of sea and swell
Figure 3.12: Lag correlation analysis for each month. The solid blue line indicates
correlation coefficient, r and dashed green line indicates probability (P) of r to
become zero for first 13 days. The x-axis indicates the time lag in days.
The values of rmax and corresponding time lag calculated for each month are given
in Table 3.5. From Figure 3.12, during the month of June r gradually increased
from negative values and reached a maximum of 0.57 at a time lag of 7.25 days.
The P value showed zero most of the time except at two lags. For September and
October months P value started from nearly zero and reached a maximum of 0.6
with a time lag of 6.8 days. During these two months P values were zero for most
of the time. During February, a highest rmax (0.83) with zero P value (among all
months) was obtained corresponding to a time lag of 7.12 days. The correlation
was statistically significant with a time lag of nearly 6 – 9 days during this month
(Figure 3.12; Month=2). The r and P values during April month were randomly
fluctuated and obtained a maximum r with a time lag of 4.38 days. During May
the initial r values were not statistically significant, but at a time lag of 4.38 days r
61
Chapter - 3 Characteristics of sea and swell
showed a maximum value. For the remaining months (Jul, Aug, Nov, Dec, Jan)
the lag was not computed due its in-significant r and P values.
The highest significant correlation in February 2010 among all months was due to
very low sea state condition over entire Indian Ocean. This sea state condition
was clearly identified in the time series plot of SWH at 90˚E longitude (figure
3.13(a)) and Spectral width parameter (ε) (figure 3.14). This indicates that in the
absence of strong wind forcing over entire TIO the variability of SWH and ETSIO
wind were correlated with a time lag of 7.12 days.
Table 3.5: Lag correlation between ETSIO winds and observed swell (Hsw).
Month
Jun-2009
Jul-2009
Aug-2009
Sep-2009
Oct-2009
Nov-2009
Dec-2009
Jan-2010
Feb-2010
Mar-2010
Apr-2010
May-2010
rmax Lag(days)
0.57
7.25
0.68
6.88
0.66
6.88
0.83
7.12
0.62
4.38
0.71
8.25
In the month of February 2010 a very low sea state condition with minimum SWH
exist over entire length of Indian Ocean i.e., form 60˚S to the northern boundary
as shown in Figure 3.13(a).
This low sea state condition allows the swell
generated over southern ocean to travel longer distance without any interference
of swell from other storm areas. The sustained wind speed with a maximum
amplitude of about 12 m/s over ETSIO is comparatively very high than that of
over BoB which is around 4 m/s (Figure 3.13(b)). However, a considerable fetch
62
Chapter - 3 Characteristics of sea and swell
of about 8 m/s wind speed exists over TSIO, which may also contribute to the
generation of swell.
Figure 3.13: Time series plot of (a ) SWH (b) wind speed at 10 m above
MSL using model data.
The time series variation of ε gives a clear understanding of the nature of the sea
state. This can be explained based on the Eqn. 3.12.
(3.12)
From the equation 3.12, the value of ε depends on Tc and Tz. Here Tc is the crest
period which counts all the crests occurred over the sea surface, whereas Tz is
zero up cross period which counts the crests crossing the mean level of the wave
profile only. If we take a smooth sine wave the value of Tc and Tz is exactly
same because every wave crosses the mean level of wave profile which results in
ε becomes zero. The value of ε approaching zero indicates a narrow band of
frequency. If a high frequency wave over riding the low frequency wave, then the
value of Tc is less than that of Tz because some waves don’t cross the mean level.
In a high sea state condition like storms, a large number of short waves with sharp
crests over ride the long swells. Hence the value of Tc becomes very small than
that of Tz, results in ε shows higher values. From figure 3.14 it was observed that
63
Chapter - 3 Characteristics of sea and swell
the values of ε were low during February 2010 among all months indicates the
existence of waves with very narrow range of frequencies.
Figure 3.14: Time series plot of Spectral width parameter (ε).
Hence from the above analysis it was observed that the influence of ETSIO winds
on SWH over TNIO was significant. The estimated time lag was 7.12 days. Some
of the results of this chapter were published (Suresh et al., 2010; Suresh et al.,
2012).
64
Chapter - 3 Characteristics of sea and swell
3.5 Summary
The seasonal characteristics of waves off east coast of India and influence of
southern ocean wind forcing were studied using buoy measurements. The analysis
showed that the average SWH during summer monsoon was highest (1.66 m)
whereas the lowest (0.6) SWH occurs during winter monsoon. The sustained
monsoon winds over a large area were responsible for the occurrence of high
wave during summer monsoon. The wave groups of sea showed nearly linear
trend for all seasons whereas the swell waves were well scattered. It was clearly
observed that the contribution of swell to the local ocean state was of very high
significance. Apart from monsoon circulation, the well identified trade winds over
south of the equator and extra tropical southern ocean storm winds were the major
sources for the occurrence of long swell. From the lag correlation analysis
between the measured swell (Hsw) and spatially averaged ETSIO wind speed
showed highest significant correlation in February 2010. Further it was also
noticed that in the absence of strong wind forcing, over entire TIO, the variability
of SWH and ETSIO wind were correlated with 7.12 days time lag. The lower
values of Spectral width parameter (ε) during this month also showed the
occurrence of narrow range (wave periods) of waves.
The present analysis also showed that the sea state in nearshore waters of
BoB was dominated by swell waves most of the time in a year. It also revealed the
variability of SWH was strongly correlated with ETSIO winds. In order to
understand the variability of SWH for full spatial extent and its responsible
forcing phenomena, it is necessary to look for spatial data. In recent time satellite
altimetry and well calibrated model simulations were providing such data. Due to
limited life time of the sensors, long time track repeativity and large swath
65
Chapter - 3 Characteristics of sea and swell
separation inhomogeneity exits with the long term data. Hence the simulated
SWH data using Wavewatch III model from NOAA was used for further analysis.
Prior to the analysis an attempt has been also made to evaluate the model data
over Indian Ocean region.
66